Year 8 Cambridge Advanced Mathematics: Quick Guide to Memorising Vocabulary and Terminology | Year 8 剑桥进阶数学：词汇术语速记指南

📚 Year 8 Cambridge Advanced Mathematics: Quick Guide to Memorising Vocabulary and Terminology | Year 8 剑桥进阶数学：词汇术语速记指南

Mastering the vocabulary of advanced mathematics at Year 8 level is essential for understanding concepts and solving problems with confidence. This guide provides memory-friendly techniques, root word analysis, and clear explanations to help you quickly learn and recall key mathematical terms. Each section pairs a term with a short memory hook so that even the most abstract words become familiar.

掌握Year 8进阶数学的词汇对于自信地理解概念和解决问题至关重要。本指南提供便于记忆的技巧、词根分析和清晰解释，帮助你快速学习和回忆关键数学术语。每一节将术语与简短的记忆钩子配对，使最抽象的词汇也变得熟悉。

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1. Number and Arithmetic Terms | 数与算术术语

Numbers are the building blocks of mathematics. Knowing exactly what to call each type of number helps you follow instructions and avoid careless mistakes. Here are the most common number categories with simple memory tricks.

数是数学的基石。确切了解每种数字类型的名称有助于你遵循指令并避免粗心错误。以下是最常见的数字类别及其简单记忆技巧。

• Integer – A whole number that can be positive, negative or zero (e.g., −5, 0, 12). Think of the word 'integral' – something complete, with no fractional or decimal part.

  整数 – 可以是正数、负数或零的整数（例如 −5，0，12）。联想 'integral'（完整的）一词，表示没有分数或小数部分。

• Rational number – Any number that can be written as a fraction a/b where a and b are integers, b ≠ 0. The word 'rational' contains 'ratio', so a rational number is a ratio.

  有理数 – 任何可以写成 a/b 形式的数，其中 a 和 b 是整数，b ≠ 0。单词 'rational' 包含 'ratio'（比），所以有理数就是可以表示为比的数。

• Irrational number – A number that cannot be written as a simple fraction (e.g., π, √2). 'Ir-' means 'not', so an irrational number is not a ratio.

  无理数 – 无法写成分数形式的数（例如 π，√2）。'Ir-' 表示“不”，所以无理数即不是比值的数。

• Numerator / Denominator – In a fraction, the numerator is the top part (north), and the denominator is the bottom part (down). Remember: 'Numerator' points to the Number of parts you have; 'Denominator' tells the Denomination (type) of parts.

  分子 / 分母 – 在分数中，分子是顶部（北）部分，分母是底部（下）部分。记住：'Numerator' 表示你拥有的部分的数量（Number）；'Denominator' 指示部分的种类（Denomination）。

• Significant figures (s.f.) – The meaningful digits in a number, starting from the first non-zero digit. Think 'Significant' = important digits that carry precision.

  有效数字 – 数字中从第一个非零数字开始的有意义的数字。联想 'Significant'（重要的），即那些携带精度的数字。

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2. Algebraic Expressions | 代数表达式

Algebra is a language of symbols. Understanding the precise vocabulary lets you translate word problems into equations and simplify expressions correctly.

代数是符号的语言。理解精确的词汇能让你将文字题转化为方程并正确地简化表达式。

• Variable – A symbol, usually a letter, that represents an unknown number. It can 'vary' its value.

  变量 – 一个符号，通常是字母，代表一个未知数。它的值可以“变化”（vary）。

• Coefficient – The number that multiplies a variable in a term (e.g., in 5x, 5 is the coefficient). 'Co-' means together; the number works together with the variable.

  系数 – 项中与变量相乘的数字（例如 5x 中，5 是系数）。'Co-' 表示“一起”；数字与变量一起运作。

• Constant – A term that has a fixed value, with no variable part. It stays 'constant' and never changes.

  常数 – 具有固定值的项，没有变量部分。它始终保持“恒定”（constant），从不改变。

• Expression – A combination of numbers, variables and operation symbols without an equals sign (e.g., 3x + 2). Think of it as a 'phrase' in the language of mathematics.

  表达式 – 数字、变量和运算符号的组合，没有等号（例如 3x + 2）。可以把它看作数学语言中的一个“短语”。

• Term – A single mathematical 'unit' in an expression, separated by + or − signs. Like the 'terms' of a contract, each part has a special role.

  项 – 表达式中由 + 或 − 号分隔的单个数学“单元”。就像合同中的“条款”（terms），每一部分都有特殊作用。

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3. Equations and Inequalities | 方程与不等式

Equations state that two things are equal; inequalities compare sizes. The symbols might look confusing, but a few visual tricks make them unforgettable.

方程表明两个事物相等；不等式则比较大小。这些符号可能看起来令人困惑，但几个视觉技巧会让你永生难忘。

• Equation – A statement that two expressions are equal, containing an equals sign (=). 'Equa-' refers to 'equal'.

  方程 – 表明两个表达式相等的陈述，包含等号（=）。'Equa-' 表示“相等”。

• Solution – A value that, when substituted for the variable, makes the equation true. It 'solves' the puzzle.

  解 – 当替换变量时能使方程成立的值。它“解决”了这个谜题。

• Inequality – showing that one quantity is greater or less than another, using symbols <, >, ≤, ≥. 'In-' means 'not'; it is not an equality.

  不等式 – 显示一个量大于或小于另一个量的关系，使用符号 <，>，≤，≥。'In-' 表示“不”；它不是等式。

• Less than < / Greater than > – Think of the symbol as a hungry crocodile's mouth: it always opens towards the larger number. (3 < 5 ∶ 3 is less than 5).

  小于 < / 大于 > – 把符号想象成饥饿鳄鱼的嘴巴：它总是朝较大的数字张开。（3 < 5 ：3 小于 5）。

• Inclusive inequality (≤ , ≥) – The extra line under the symbol means 'or equal to', so the boundary value is included. The line acts like a 'floor' that keeps the number inside.

  包含等式的不等式（≤ , ≥） – 符号下方的额外横线表示“或等于”，因此边界值被包含在内。这条线就像一块“地板”，把数字留在里面。

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4. Factors, Multiples and Primes | 因数、倍数与质数

These terms describe how numbers relate to each other through multiplication and division. Mastering them will make fractions, HCF and LCM problems much easier.

这些术语描述了数字通过乘法和除法相互联系的方式。掌握它们将使分数、最高公因数和最小公倍数问题变得容易得多。

• Factor – A whole number that divides another number exactly, leaving no remainder. A factor 'fits' perfectly into the number. (Factors of 12: 1, 2, 3, 4, 6, 12).

  因数 – 能整除另一个数且没有余数的整数。因数完美地“嵌入”该数中。（12 的因数：1，2，3，4，6，12）。

• Multiple – The result of multiplying a number by any whole number. Multiples are like 'many copies' of that number. (Multiples of 5: 5, 10, 15, 20...).

  倍数 – 某数乘以任意整数的结果。倍数就像是该数的“许多份”。（5 的倍数：5，10，15，20……）。

• Prime number – A number greater than 1 that has exactly two distinct factors: 1 and itself. Think 'primary' or 'first' – it cannot be broken down further. (2, 3, 5, 7, 11...).

  质数（素数） – 大于 1 且恰好只有两个不同因数的数：1 和它自身。联想“primary”（基本的）——它无法再分解。（2，3，5，7，11……）。

• Composite number – A number with more than two factors. 'Composite' means 'made up of parts', just like a composite material. (4, 6, 8, 9, 10...).

  合数 – 拥有两个以上因数的数。'Composite'（复合的）意味着“由部分组成的”，就像复合材料一样。（4，6，8，9，10……）。

• HCF (Highest Common Factor) / LCM (Lowest Common Multiple) – HCF is the largest factor shared by two or more numbers; LCM is the smallest multiple they share. Think 'Highest' for factor, 'Lowest' for multiple – opposites attract.

  HCF（最高公因数）/ LCM（最小公倍数） – HCF 是两个或多个数共有的最大因数；LCM 是它们共有的最小倍数。因数用“最高”，倍数用“最低”——相反相吸。

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5. Ratio, Proportion and Percentage | 比、比例与百分数

Comparisons are at the heart of many real-world problems. Ratio, proportion and percentage are three ways of expressing relationships between quantities.

比较是许多现实世界问题的核心。比、比例和百分数是表达数量之间关系的三种方式。

• Ratio – A comparison of two or more quantities of the same kind, often written as a:b. 'Ratio' is Latin for 'reckoning' or 'calculation'.

  比 – 对两个或多个同类数量的比较，常写作 a:b。'Ratio' 在拉丁语中意为“推算”或“计算”。

• Proportion – A statement that two ratios are equal, e.g., a/b = c/d. 'Pro-' means 'for', and 'portion' means part – proportion compares parts.

  比例 – 两个比相等的陈述，例如 a/b = c/d。'Pro-' 意为“对于”，'portion' 意为部分——比例比较部分。

• Direct proportion – When one quantity increases, the other increases at the same rate (y = kx). They move 'directly' together.

  正比例 – 当一个量增加时，另一个量以相同速率增加（y = kx）。它们“直接”同步移动。

• Inverse proportion – When one quantity increases, the other decreases in a related way (y = k/x). 'Inverse' means turned around.

  反比例 – 当一个量增加时，另一个量以相关的方式减少（y = k/x）。'Inverse' 意思是颠倒过来。

• Percentage – A fraction with denominator 100, denoted by %. 'Per cent' means 'out of 100' (cent = hundred, like century).

  百分数 – 分母为 100 的分数，用 % 表示。'Per cent' 意为“每一百”（cent = 百，像 century 世纪一样）。

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6. Statistics and Data Handling | 统计与数据处理

Statistics uses numbers to tell stories. The vocabulary here helps you describe data sets and make sense of averages and spread.

统计用数字讲述故事。这里的词汇帮助你描述数据集并理解平均数与离散程度。

• Mean – The sum of all values divided by the number of values. Also called the average. 'Mean' is what you 'mean' by typical.

  平均数（均值） – 所有数值的总和除以数值的个数。也称算术平均。'Mean' 就是你所说的“典型”。

• Median – The middle value when data is arranged in order. Think 'middle' and 'media' (in the middle of a road).

  中位数 – 数据按顺序排列后的中间值。联想“middle”（中间）和道路中的“median”（隔离带）。

• Mode – The value that appears most often. 'Mode' sounds like 'most'; it is the most frequent.

  众数 – 出现频率最高的值。'Mode' 听起来像 'most'（最多）；它就是最常出现的。

• Range – The difference between the largest and smallest values. It shows how 'far ranging' the data is.

  极差（范围） – 最大值与最小值之间的差值。它显示了数据的“范围”有多广。

• Discrete data / Continuous data – Discrete data can only take specific values (e.g., number of students – you cannot have half a student). Continuous data can take any value within a range (e.g., height, temperature). 'Discrete' means separate, 'continuous' means connected.

  离散数据 / 连续数据 – 离散数据只能取特定值（例如学生人数——不可能有半个学生）。连续数据可以在一个范围内取任意值（例如身高，温度）。'Discrete' 意味着分开的，'continuous' 意味着连接的。

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7. Geometry Basics | 几何基础

Geometry is the study of shapes and space. Basic geometric terms are used constantly, so a firm grasp of their definitions is crucial.

几何是研究形状和空间的学科。基本的几何术语被持续使用，因此牢固掌握它们的定义至关重要。

• Point – An exact location in space; it has no size. Think of the sharp 'point' of a pencil.

  点 – 空间中的精确位置；没有大小。想象铅笔的锋利“尖端”。

• Line – A straight one-dimensional figure extending infinitely in both directions. A 'line' has no ends.

  直线 – 一个笔直的一维图形，两端无限延伸。一条“线”没有端点。

• Line segment – A part of a line with two endpoints. A 'segment' is a piece cut from the whole.

  线段 – 直线的一部分，有两个端点。'Segment'（段）是从整体切下的一部分。

• Ray – A part of a line that starts at one endpoint and goes on forever in one direction. Like a 'ray' of light from a torch.

  射线 – 直线的一部分，从一个端点开始并沿一个方向无限延伸。就像手电筒发出的“光线”（ray）。

• Parallel lines – Lines in a plane that never meet, the same distance apart. 'Parallel' comes from Greek 'para' (beside) and 'allelois' (each other).

  平行线 – 平面内永不相交、距离相等的直线。'Parallel' 源自希腊语 'para'（旁边）和 'allelois'（彼此）。

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8. Angles and Lines | 角与线

Angles are formed when two lines meet, and their names tell you exactly how wide they open. Learning angle vocabulary unlocks angle calculation problems.

当两条线相遇时会形成角，它们的名称准确地告诉你它们张开的程度。学习角的词汇可以解锁角度计算问题。

• Acute angle – An angle less than 90°. 'Acute' means 'sharp' – a small, sharp angle.

  锐角 – 小于 90° 的角。'Acute' 意为“尖锐”——一个小的、尖锐的角。

• Right angle – Exactly 90°, often marked with a small square. It is the 'right' (correct) angle for a corner.

  直角 – 恰好 90°，通常用小方框标记。它是墙角等“正确”的角度。

• Obtuse angle – An angle between 90° and 180°. 'Obtuse' means 'blunt' or 'dull' – a wide, blunt angle.

  钝角 – 介于 90° 和 180° 之间的角。'Obtuse' 意为“钝的”——一个宽而钝的角。

• Reflex angle – An angle greater than 180° but less than 360°. Think of a reflex action – it bends backwards.

  优角（反射角） – 大于 180° 但小于 360° 的角。联想反射动作——它向后弯曲。

• Complementary / Supplementary angles – Complementary pairs sum to 90° (Complete a right angle), supplementary pairs sum to 180° (a Straight line). Memory hook: C before S, 90 before 180.

  余角 / 补角 – 余角对加起来为 90°（补成一个直角），补角对加起来为 180°（补成一条直线）。记忆钩子：C 在 S 前，90 在 180 前。

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9. Triangles and Polygons | 三角形与多边形

Triangles and other polygons are classified by their sides and angles. The names often use Greek or Latin number prefixes, which are easy to learn.

三角形和其他多边形根据边和角进行分类。其名称常使用希腊或拉丁数字前缀，这些前缀很容易学习。

• Equilateral triangle – All three sides equal. 'Equi-' = equal, 'lateral' = side.

  等边三角形 – 三条边全等。'Equi-' = 等，'lateral' = 边。

• Isosceles triangle – Two equal sides. 'Isos' (Greek: equal) + 'skelos' (leg).

  等腰三角形 – 两条边相等。'Isos'（希腊语：相等）+ 'skelos'（腿）。

• Scalene triangle – All sides different. 'Scalene' means 'uneven', like a limp.

  不等边三角形 – 所有的边都不相等。'Scalene' 意为“不平坦的”，像跛行一样。

• Polygon – A closed 2D shape with straight sides. 'Poly-' = many, 'gon' = angle (think pentagon, hexagon, etc.).

  多边形 – 由直边组成的封闭二维图形。'Poly-' = 多，'gon' = 角（联想 pentagon 五边形，hexagon 六边形等）。

• Quadrilateral – A four-sided polygon. 'Quadri-' = four, 'lateral' = side. Family includes square, rectangle, parallelogram, rhombus, trapezium, kite.

  四边形 – 有四条边的多边形。'Quadri-' = 四，'lateral' = 边。包括正方形、矩形、平行四边形、菱形、梯形、风筝形。

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10. Perimeter, Area and Volume | 周长、面积与体积

Measuring the size of shapes involves perimeter (the boundary), area (the surface) and volume (the space inside). The units are as important as the numbers.

衡量图形的大小涉及周长（边界）、面积（表面）和体积（内部空间）。单位与数字同样重要。

• Perimeter – The total distance around a 2D shape. 'Peri-' = around, 'meter' = measure.

  周长 – 绕二维图形一周的总距离。'Peri-' = 周围，'meter' = 测量。

• Area – The amount of surface a shape covers, measured in square units (cm², m²). Think of an open 'area' of land.

  面积 – 图形所覆盖的表面大小，以平方单位（cm²，m²）计量。想象一块开阔的“区域”（area）。

• Volume – The amount of space a 3D object occupies, measured in cubic units (cm³, m³). Like the volume of a loudspeaker – it fills space.

  体积（容积） – 三维物体所占据的空间大小，以立方单位（cm³，m³）计量。就像扬声器的音量（volume）——它充满空间。

• Surface area – The total area of all faces of a 3D solid. It is the 'skin' area you could paint.

  表面积 – 三维立体所有面的总面积。它是你可以涂上颜色的“皮肤”面积。

• Compound shape – A shape made by joining two or more simple shapes. 'Compound' means made up of components.

  复合图形 – 由两个或更多简单图形组合而成的形状。'Compound' 意味着由组成部分构成。

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11. Transformations and Symmetry | 变换与对称

Transformations move or change shapes according to rules, while symmetry describes balance. These concepts are key in both coordinates and geometry.

变换根据规则移动或改变图形，而对称性描述平衡。这些概念在坐标和几何中都很关键。

• Translation – A 'slide' moving a shape without turning or flipping, described by a vector. 'Trans-' = across, 'lat' = carry – to carry across.

  平移 – 不旋转、不翻转地“滑动”一个图形，用向量描述。'Trans-' = 跨越，'lat' = 携带——搬运过去。

• Reflection – A 'flip' over a mirror line. The image is the same distance behind the mirror as the object in front. 'Reflect' means to bend back, like light.

  反射（翻转） – 沿镜像线的“翻转”。影像在镜后的距离与物体在镜前的距离相等。'Reflect' 意为折回，像光线一样。

• Rotation – A 'turn' around a fixed centre. Specified by angle, direction and centre. 'Rotate' shares the root with 'rotor', meaning wheel.

  旋转 – 绕一个固定中心的“转动”。由角度、方向和中心指定。'Rotate' 与 'rotor'（转子）共享词根，意为轮子。

• Enlargement – A change in size by a scale factor about a centre. 'Enlarge' means make larger (scale factor > 1 makes bigger; 0 < scale factor < 1 makes smaller).

  放大（位似变换） – 通过相对于一个中心的比例因子改变大小。'Enlarge' 意为变大（比例因子 > 1 变大；0 < 比例因子 < 1 变小）。

• Line symmetry / Rotational symmetry – lves match. Rotational symmetry means it looks the same more than once during a full turn. 'Symmetry' = 'same measure'.

  线对称 / 旋转对称 – 如果一个图形可以沿着某条线折叠使两半完全重合，那么它具有线对称。旋转对称意味着在完整旋转过程中图形会多次看起来与自身重合。'Symmetry' = “相同的度量”。

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12. Probability | 概率

Probability measures how likely an event is to happen. The vocabulary is precise, from impossible to certain, and uses fractions, decimals or percentages.

概率衡量事件发生的可能性大小。词汇从确定到不可能都用精确的分数、小数或百分数来表示。

• Probability scale – A number line from 0 to 1 where 0 = impossible, 1 = certain. Think of 0% chance to 100% chance.

  概率尺度 – 从 0 到 1 的数轴，0 = 不可能，1 = 必然。想象从 0% 的可能性到 100% 的可能性。

• Experiment / Trial – An experiment is a repeatable process with observable outcomes (e.g., rolling a die). Each repeat is a trial.

  实验 / 试验 – 实验是一个可重复的过程，具有可观察的结果（例如掷骰子）。每次重复是一次试验。

• Outcome / Event – An outcome is a possible result. An event is a set of one or more outcomes. 'Event' is a collection of outcomes you care about.

  结果 / 事件 – 结果是可能发生的结果。事件是一个或多个结果的集合。'事件' 是你关心的结果的集合。

• Sample space – The set of all possible outcomes. The 'sample' is everything that

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